Quantum field theory on noncommutative spaces
Abstract
A pedagogical and selfcontained introduction to noncommutative quantum field theory is presented, with emphasis on those properties that are intimately tied to string theory and gravity. Topics covered include the WeylWigner correspondence, noncommutative Feynman diagrams, UV/IR mixing, noncommutative YangMills theory on infinite space and on the torus, Morita equivalences of noncommutative gauge theories, twisted reduced models, and an indepth study of the gauge group of noncommutative YangMills theory. Some of the more mathematical ideas and techniques of noncommutative geometry are also briefly explained.
 Publication:

Physics Reports
 Pub Date:
 May 2003
 DOI:
 10.1016/S03701573(03)000590
 arXiv:
 arXiv:hepth/0109162
 Bibcode:
 2003PhR...378..207S
 Keywords:

 High Energy Physics  Theory;
 Condensed Matter;
 General Relativity and Quantum Cosmology;
 High Energy Physics  Lattice;
 High Energy Physics  Phenomenology;
 Mathematical Physics;
 Mathematics  Quantum Algebra
 EPrint:
 111 pages LaTeX, 6 eps figures